Monte Carlo (MC) simulations of the full detector, based on geant4 [1]}
simulation software, and the BESIII Object Oriented Simulation Tool
(BOOST) [2]}, are used
to optimize the event selection criteria, understand potential backgrounds,
and determine the detection efficiency. The BOOST package contains the detector geometry
and material description, the detector response and signal digitization models,
as well as records of the detector running conditions and performance.
Large inclusive MC samples at \(\sqrt{s}=2.1250\)  and 2.3960 GeV are generated to estimate potential backgrounds.
The processes \(e^+e^-\rightarrow e^+e^-, \mu ^+\mu ^-\)  and \(\gamma \gamma \)  are generated with the Babayaga
generator [3]}, while \(e^+e^- \rightarrow \)  hadrons and two photon processes are simulated by
the luarlw [4]} and bestwogam [5]} generators, respectively.
Due to the dominance of \(\rho \eta ^{\prime }\)  in \(e^+e^- \rightarrow \eta ^\prime \pi ^{+}\pi ^{-}\) 
process [6]}, the signal MC is
generated with conexc [7]} as \(e^+e^- \rightarrow \rho \eta ^\prime \) .
The cross sections measured by the BABAR experiment [6]}
are used as initial input.
The ISR, vacuum polarization and the angular distributions of the final state have been taken
into account in the generator.
The wide \(\rho \)  resonance in the intermediate state is described by the Gounaris-Sakurai (GS) model [9]}.
The \(\eta ^\prime \rightarrow \gamma \pi ^{+}\pi ^{-}\)  decay is simulated with a model
based on the results of the amplitude analysis in Ref. [10]},
and the \(\eta ^\prime \rightarrow \eta \pi ^{+}\pi ^{-}\)  decay is produced
using a phase-space (PHSP) model.
